<![CDATA[This study investigates the differential cross-section (DCS) for laser-assisted positron-electron scattering in a Gaussian wave packet, within a linearly polarized laser field in a thermal environment. For this, a theoretical model was developed with a designed thermal Gaussian Volkov wavefunction, vector potential, and scattering matrix with the application of the Bessel function. The developed model was computed using the Matlab programming language to study the nature of the developed model of DCS. The observation shows that the DCS initially increases with positron energy, reaching a peak around 0.5 eV; after that, it decreases with further increases in energy and approaches a constant at high energies. This is due to changing dynamics of positron-electron interactions with resonance occurring at specific energies. Also, the observation shows that temperature plays a significant role, especially at lower energies, with higher temperatures (325 K) enhancing the DCS due to increased thermal excitation of the target electrons. The study also explores the influence of the z-value and found that higher z-values lead to a decrease in the DCS due to the Coulombic interaction becoming stronger. Moreover, the effects of external factors such as the number of laser field photons and pulse duration are considered. The observation shows that shorter laser pulse durations and higher photon energies enhance the scattering process, while longer pulse durations result in a decrease in DCS. This study aids in optimizing technologies like PET imaging, plasma diagnostics, and particle accelerators by revealing how positron-electron scattering varies with energy, temperature, and laser parameters. It supports real-world applications in medical, space, and materials science.]]>
